1. Field of the Invention
The invention relates to a game board, usually provided with a set of playing pieces for the purpose of playing a game in which the relationship between the areas on the board is relevant to the game's characteristics.
2. Prior Art
Many such games are already in existence, some of them being popular solely for purposes of entertainment (such as backgammon), some being educational as well (such as chess or reversi). Though the boards presented in this invention are useful for games of both categories, this invention widely expands the set of possibilities for other such games, and presents two other such games as examples.
Probably the closest prior art to the uniformity aspect of this invention is U.S. Pat. No. 4,005,868, titled "Puzzle" (in which the claims, stating that each board would have a number of points between areas corresponding to the number of vertices on a polyhedron whose faces the areas represent, contradicted the illustrations, all of which had more points than the number of vertices on its represented polyhedron, unless the entire circles containing the outer points were to be considered to be single points, which circles containing a plurality of points are not and should therefore not be considered to be), which although it presents an uncountably infinite variety of boards which can be viewed as having a quality of uniformity (to be described in further detail hereinafter; the "Puzzle" inventor did not in fact define his boards with this view of them in mind, as in order to obtain this view, one must consider the lines which he described as lines from areas to vertices to be themselves borders of areas) similar to the uniformity that is one aspect of this invention (for which reason the uniformity in this invention was defined to exclude those defined by the "Puzzle" patent), presents only an infinitesmal (though perhaps countably infinitesmal) fraction of the uncountably infinite variety of boards having this quality. The invention described herein presents an uncountably infinite variety of configurations which is at least infinitely greater (if not uncountably infinitely greater) than the variety of boards of the "Puzzle" invention, having a similar, though not equivalent, quality (In some cases the uniformity is more pure; in other cases it is less). Also, the "Puzzle" includes boards which do not have this uniformity at all (the "Puzzle" inventor only gave examples of mappings for regular polyhedrons, but did not limit his claims to mappings of regular polyhedrons, and only a mapping for a regular polyhedron would have this uniformity).